The minimum residual method (MINRES) of Paige and Saunders (1975), which is often the method of choice for symmetric linear systems, is a generalization of t...

We propose an iterative method named USYMLQR for the solution of symmetric saddle-point systems that exploits the orthogonal tridiagonalization method of Sa...

We propose a regularization method for nonlinear least-squares problems with equality constraints. Our approach is modeled after those of Arreckx and Orban ...

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was ...

We describe LNLQ for solving the least-norm problem $\min\ \|x\|$ subject to $Ax=b$. Craig's method is known to be equivalent to applying the conjug...

We propose an infeasible interior-point algorithm for constrained linear least-squares problems based on the primal-dual regularization of convex program...

We propose a factorization-free method for equality-constrained optimization based on a problem in which all constraints are systematically regularized. ...

For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly-constrained (LCL) augmented-La...

We consider the solution of derivative-free optimization problems with continuous, integer, discrete and categorical variables in the context of costly black...

We study X-ray tomograqphic reconstruction using statistical methods. The problem is expressed in cylindrical coordinates, which yield significant computatio...

Stochastic Dynamic Programming (SDP) is a powerful approach applicable to nonconvex and stochastic stagewise problems. We investigate the impact of the form...

We propose an iterative method named LSLQ for solving linear least-squares problems $A x \approx b$ of any shape. The method is based on the Golub and K...

For positive definite linear systems (or semidefinite consistent systems), we use Gauss-Radau quadrature to obtain a cheaply computable upper bound on the ...

NLP.py is a programming environment to model continuous optimization problems and to design computational methods in the high-level and powerful Python l...

We describe a collection of linear systems generated during the iterations of an interior-point method for convex quadratic optimization. As the iteration...

Adaptative cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems with a shifted Hessian in the spirit of the mo...

In many large engineering design problems, it is not computationally feasible or realistic to store Jacobians or Hessians explicitly. Matrix-free implementat...

A preconditioned variant of the Golub and Kahan (1965) bidiagonalization process recently proposed by Arioli (2013) and Arioli and Orban (2013) allows us to ...

We propose a generalization of the limited-memory Cholesky factorization of Lin and Moré (1999) to the symmetric indefinite case with special interest in sym...

Symmetric quasi-definite systems may be interpreted as regularized linear least-squares problem in appropriate metrics and arise from applications such as re...